Asked by rr
Solve for the sum of series in given sequence
S(sub)5 in { 10, 30, 90, 270, 810, 2430}
S(sub)5 in { 10, 30, 90, 270, 810, 2430}
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GPT 3.5
To find the sum of the series in the given sequence, we can use the formula for the sum of a geometric series:
S = a * (1 - r^n) / (1 - r)
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term (a) is 10, and the common ratio (r) is 3 (each term is obtained by multiplying the previous term by 3). The number of terms (n) is 5.
Plugging these values into the formula, we get:
S = 10 * (1 - 3^5) / (1 - 3)
= 10 * (1 - 243) / (1 - 3)
= 10 * (-242) / (-2)
= 10 * 121
= 1210
So the sum of the series S5 = { 10, 30, 90, 270, 810, 2430} is 1210.
S = a * (1 - r^n) / (1 - r)
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, the first term (a) is 10, and the common ratio (r) is 3 (each term is obtained by multiplying the previous term by 3). The number of terms (n) is 5.
Plugging these values into the formula, we get:
S = 10 * (1 - 3^5) / (1 - 3)
= 10 * (1 - 243) / (1 - 3)
= 10 * (-242) / (-2)
= 10 * 121
= 1210
So the sum of the series S5 = { 10, 30, 90, 270, 810, 2430} is 1210.
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